Title: Almost Ricci-flat 4-manifolds

Abstract: A manifold is almost Ricci-flat if it admits a sequence of Riemannian
metrics with diameter one, for which the Ricci curvature goes to zero
uniformly.  I will describe results about the topology and geometry of
almost Ricci-flat 4-manifolds in the noncollapsed case (joint work with
Vitali Kapovitch) and in the collapsed case.